One constant pain point for all users, regardless of your technical expertise, is managing the passwords for the vast number of sites you can accumulate over the years. With a family, suddenly this can grow exponentially with every addition of a family member. Throw in the guidelines for password strength of memorised passwords, as recommended by the National Institute of Standards and Technology (NIST), things can get messy real quick. A great summary can be found here.
This post provides some guidelines you can use for you and your family.
Use an Password Manager application to manage your passwords
There are various password manager applications available (some free) that will help you manage your password. Some examples are Keeper and LastPass. An evaluation and comparison of Password Managers is outside the scope of this post but you should be able to find other sites you can refer to.
If you are an Apple user (iPhone, iPad, Mac OS X) you can refer to my post Managing your passwords for Apple users for free. As far as I am aware there is not native way of storing password easily on Windows (without installing any third party apps). Happy to be corrected, just comment in the page below.
Use unique passwords for each of your sites.
Use a different password for each of your accounts, re-using passwords is risky. If someone figures out your password for one account, it's possible they could get access to your personal information, or other online services like shopping or banking. This also reduces the chances of identity theft and ransom attacks by hackers.
There are some sites available that will generate a password for you, just ensure they are reputable. One such site is Norton by Symantec's Password Generator.
Use your browser to remember your passwords
With the services now being provided by major browser vendors its possible to simple login to the service via your browser as explained below and prevents the need continuously reference your passwords. Or worse, fall into bad habits such as using the same password for multiple sites.
I highly recommend you create unique login's for each of your users which will ensure only the person who is authorised to the site has access. It's also important to secure your own user login with an appropriate password that no one else knows.
Google Chrome browser
Google has Smart Lock which you can access as part of creating a Google Account. This allows you to sync passwords across multiple devices. You can also manage save passwords from the web by visiting https://passwords.google.com/
Apple Safari browser
Teach your children about the importance of Password Management
I've posted previously on how you can use Apples Notes to secure information. Since then I've been teaching my older children how they can mange their own passwords. The age you would want to do this depends on your child so you will need to make a judgement call.